Competitive trapping in complex state spaces

In complex state space dynamics at finite time scales, the trapping in certain regions of state space is of great importance, e.g. in the field of protein folding or in the application of stochastic global optimization algorithms. Here, we analyze the influence of the density of states on the features of the trapping process. In particular, we compare the trapping power of a valley with a power-law density of states to one with an exponentially growing density of states. The outcome of this competition crucially depends on the annealing speed and shows that the clear difference between these two paradigmatic densities of states observed at very slow (near-equilibrium) annealing is lost for fast non-equilibrium processes, and that the outcome of the relaxation can strongly depend on the time scale of the process and subtle features of the density of states.